Sphere Calculator

Find a sphere’s volume and surface area from its radius or diameter. Already know the volume or surface area? Use it to calculate the radius and other measurements.

Calculate Your Sphere

Choose one known measurement. The calculator finds the dimensions of a complete sphere.

Radius runs from the center to any point on the sphere’s surface.

Sphere with radius and diameter A sphere shown in perspective. Radius runs from its center to the surface; diameter passes through the center. r d O
Every surface point is the same distance from the center. Diameter = 2 × radius. Diagram is not to scale.

Changing the input unit converts your measurement. Changing the known measurement clears the input so you can enter the new quantity.

A sphere is three-dimensional. For the area inside a flat circular outline, use the circle area calculator .

QUICK START

How to Use the Sphere Calculator

One known measurement is enough to calculate a complete sphere’s volume, surface area and dimensions.

  1. Select what you know

    Choose radius, diameter, volume or surface area. Use radius for the distance from center to surface, or diameter for the distance across the sphere through its center.

  2. Enter the value in its matching unit

    Enter a positive number. Radius and diameter use length units, surface area uses squared units, and volume uses cubic units. For example, enter a known volume in cm³ rather than cm.

  3. Choose output units and precision

    Select the unit for your results and two, four or six decimal places. Changing the input unit converts the known measurement; output units control how the calculated results are displayed.

  4. Follow the radius calculation

    When you enter volume or surface area, the tool first finds the radius. Review that working, then check the remaining results and select Copy Result to copy them.

Use the complete sphere measurement: Surface area means the entire curved exterior, rather than the area of a circular slice. For the area of a circle through the sphere’s center, use the same radius in the circle area calculator .

WORKED EXAMPLES

Sphere Calculations Step by Step

Follow these examples to calculate a sphere’s volume and surface area, or work backward from its volume to find the radius. Decimal answers are rounded to four places.

EXAMPLE 01 · RADIUS

Find volume and surface area from a radius

A sphere has a radius of 5 centimeters. Use this measurement directly in the volume and surface area formulas.

GIVEN MEASUREMENTS
Radius (r)
5 cm
Diameter (2r)
10 cm
  1. Substitute the radius into the volume formula

    V = (4 ÷ 3) × π × r³

    V = (4 ÷ 3) × π × 5³

  2. Simplify the volume

    V = (500π ÷ 3) cm³

    V ≈ 523.5988 cm³

  3. Calculate the outer surface area

    A = 4 × π × 5² = 100π cm²

    A ≈ 314.1593 cm²

RESULT Volume ≈ 523.5988 cm³

Surface area ≈ 314.1593 cm²

EXAMPLE 02 · DIAMETER

Calculate a sphere’s volume from its diameter

A spherical ball measures 12 inches across its center. Divide the diameter by two before using the radius formulas.

GIVEN MEASUREMENTS
Diameter (d)
12 in
Radius (d ÷ 2)
6 in
  1. Find the radius

    r = d ÷ 2

    r = 12 ÷ 2 = 6 in

  2. Calculate the volume

    V = (4 ÷ 3) × π × 6³

    V = 288π in³ ≈ 904.7787 in³

  3. Calculate the surface area

    A = 4 × π × 6² = 144π in²

    A ≈ 452.3893 in²

RESULT Volume ≈ 904.7787 in³

Surface area ≈ 452.3893 in²

What if you know the volume instead?

Rearrange the formula to r = ∛(3V ÷ 4π). For a volume of 36π cm³, r = ∛[(3 × 36π) ÷ 4π] = ∛27 = 3 cm. The diameter is therefore 6 cm. Select Volume in the sphere calculator and enter approximately 113.0973355 cm³ to try this calculation.

Check your units: Radius and diameter are lengths, surface area is measured in square units, and volume is measured in cubic units. Keep π in your working until the final step to avoid rounding too early.

UNDERSTAND THE FORMULAS

Sphere Volume and Surface Area Formulas

Use the radius to calculate the space inside a sphere and the area of its curved surface. If you know the diameter, divide it by two first.

r V = (4 ÷ 3) × π × r³
Volume: the space inside Cube the radius, then multiply by four-thirds and π. The result uses cubic units, such as cm³.
A = 4 × π × r²
Surface area: the curved outside Square the radius, then multiply by 4π. The result uses square units, such as cm².
r = radius, d = diameter, V = volume, A = surface area, and C = great-circle circumference. Illustrations are not drawn to scale.
Measurement Formula Units
Volume from radius V = (4 ÷ 3) × π × r³ Cubic, e.g. cm³
Volume from diameter V = π × d³ ÷ 6 Cubic, e.g. cm³
Surface area from radius A = 4 × π × r² Square, e.g. cm²
Surface area from diameter A = π × d² Square, e.g. cm²
Radius from volume r = ∛(3V ÷ 4π) Length, e.g. cm
Radius from surface area r = √(A ÷ 4π) Length, e.g. cm
Diameter d = 2r Length, e.g. cm
Great-circle circumference C = 2 × π × r Length, e.g. cm

Size changes affect area and volume differently

Doubling a sphere’s radius makes its surface area four times larger and its volume eight times larger. This follows from the squared radius in the area formula and the cubed radius in the volume formula.

A great circle is a cross-section

A flat cut through the center produces a circle with the same radius as the sphere. Its circumference is 2πr, while the sphere’s entire curved surface area is 4πr². The guide lines in the diagrams are not edges.

These formulas apply to a complete sphere. For a visual explanation of the shape and its calculations, explore the sphere guide on Math Is Fun.

COMMON QUESTIONS

Frequently Asked Questions

Answers about sphere measurements, unit conversions, hollow shapes and using the calculator’s results.

Can I calculate a sphere using only its diameter?

Yes. Select Diameter and enter the distance across the sphere through its center. The calculator uses r = d ÷ 2 to find the radius, then calculates volume and surface area. Volume can also be calculated directly with V = πd³ ÷ 6.

How do I find the radius from volume or surface area?

For a known volume, use r = ∛(3V ÷ 4π). For a known surface area, use r = √(A ÷ 4π). Select the measurement you know and its matching unit: cubic units for volume or square units for surface area. The calculator derives the radius and the remaining measurements of the sphere.

Does changing the unit change the sphere’s size?

Changing the input unit converts a valid entered value to represent the same measurement. For example, a 10 cm radius becomes 100 mm. The output unit changes how the results are displayed. Switching the measurement type, such as radius to volume, clears the input so you can enter the new measurement.

Why do surface area and volume use different units?

Surface area measures a two-dimensional surface, so it uses square units such as cm². Volume measures three-dimensional space, so it uses cubic units such as cm³. Their numerical values can occasionally match, but they describe different quantities and cannot be treated as interchangeable.

Can I use the results for a hemisphere?

The calculator returns measurements for a complete sphere. For a hemisphere with the same radius, halve the volume: V = (2 ÷ 3)πr³. Its curved surface area is 2πr². Including the flat circular base gives a total surface area of 3πr².

How do I calculate the material in a hollow sphere?

Calculate the volume using the outer radius, then repeat using the inner radius. Subtract the inner volume from the outer volume: V = (4 ÷ 3)π(R³ − r³). Here, R is the outer radius and r is the inner radius. Use the same units for both. This gives the shell’s material volume rather than its internal capacity.

Can I convert the volume result to liters?

Yes. Divide a volume in cubic centimeters by 1,000 to get liters, or multiply a volume in cubic meters by 1,000. For a hollow spherical container’s internal capacity, calculate using its inner radius rather than its outside radius.

Will this work for an oval or irregular ball?

The formulas assume a perfect sphere, whose surface is the same distance from the center in every direction. A noticeably stretched or flattened shape needs ellipsoid or spheroid formulas. For a nearly spherical object, the result is an approximation whose accuracy depends on its shape and your measurement.

PUT YOUR MEASUREMENT TO WORK

Find Your Sphere’s Volume and Surface Area

Start with a radius, diameter, volume or surface area. Get the remaining sphere measurements in your preferred units, with calculation steps you can follow.

Use Sphere Calculator